Locus problems

PQRS is a variable rectangle inside the triangle ABC where PS is on the x-axis
and Q,R are on sides AC and AB respectively. Let the length of RS be h.
a. Find the coordinates of Q and R in terms of h.
b. Let A1 be the area of ABC, A2 be the maximum possible area of rectangle
PQRS and A3 be the area of PQRS when it is a square. Find A1, A2 and A3.
c. The diagonals of PQRS meet at M(x,y). Express x and y in terms of h.
Hence find the equation of the locus of M.